Uniformly spaced linear array ULA

1. The problem statement, all variables and given/known data

A one dimensional linear array of 10 sensors spaced d=lambda/2 apart from each other. Desired signal and interference are pure sinusoidal with the same frequency, lambda is the wavelength. Desired signal coming from the foresight and interference coming from and angle of 50 degrees. The signal to interference ratio is -30dB, the signal to noise ratio is -10dB.

a) Compute the optimal weights of the array using MVDR.

b) Compute and plot the antenna pattern

c) Compute the SIR Out

d)Compute the array antenna output power, interference power and noise power.





3. The attempt at a solution



a) This is straightforward use of the equation.



b) I plotted the antenna pattern by 10*log10(abs(weight'*matrix of of signal)), but I read somewhere the dB is to be coverted by 20*log10. My answer with 20*log10 does not equal to what my teacher said it would, but with 10*log10 it does.



I am confused what it means by compute the antenna pattern. My teacher said it is the hermitian of the optimal weight times *matrix of pure sinusoidal * optimal weight , but this yields a scalar number.



d)

power of interference is hermitian of optimal weight* covariance matrix of interference *optimal weight



power of noise is hermitian of optimal weight*covariance matrix of noise *optimal weight



power of signal is hermitian of optimal weight*covariance matrix if signal * optimal weight



so for c)



SIR out would be power of signal / power of interference from part d



Is this all correct?

Also What does negative processing gain imply?